Sliced Wasserstein

Sliced Wasserstein (SW) distance offers a computationally efficient approximation of the Wasserstein distance, a powerful metric for comparing probability distributions. Current research focuses on improving SW's accuracy and scalability through techniques like quasi-Monte Carlo integration, control variates, and novel slicing operators tailored to diverse data types (e.g., spherical data, high-dimensional point clouds, and matrices). These advancements enable SW's application in various fields, including generative modeling, domain adaptation, and comparisons of complex data structures where traditional optimal transport methods are computationally prohibitive. The resulting improvements in efficiency and applicability are significantly impacting machine learning and related areas.